Influence of Active-to-Passive Ratio on the Deformation in Circular Dielectric Elastomer Actuators.

To further improve the performance of dielectric elastomer actuaotrs (DEAs), the development of novel elastomers with enhanced electro-mechanical properties is focal for the advancement of the technology. Hence, reliable techniques to assess their electro-mechanical performance are necessary. Characterization of the actuator materials is often achieved by fabricating circular DEAs with the pre-stretch of the membrane fixed by a stiff frame. Because of this set-up, the electrode size relative to the carrier frame's dimension has an impact on actuator strain and displacement. To allow for comparable results across different studies, the influence of this effect needs to be quantified and taken into account. This paper presents an in-depth study of the active-to-passive ratio by proposing two simplified analytical models for circular DEA and comparing them. The first model is taking the hyperelastic material properties of the dielectric film into account while the second model is a linear elastic lumped parameter model based on the electro-mechanical analogy. Both models lie in good agreement and show a significant linear impact of the radial active-to-passive ratio on the electro-active strain and a resulting maximum of displacement around 50% radial coverage ratio. These findings are validated by experiments with actuators fabricated using silicone membranes. It is shown that the electrode size is not only an important parameter in the experimental design, but in some cases of higher significance for the accuracy of analytical models than the hyperelastic properties of the material. Furthermore, it could be shown that a radial coverage ratio of around 50% is desirable when measuring displacement as it maximizes the displacement and lowers the impact of deviations in electrode sizes due to fabrication errors.